"""
1021. Remove Outermost Parentheses

A valid parentheses string is either empty (""), "(" + A + ")", or A + B, where A and B are valid parentheses strings,
and + represents string concatenation.  For example, "", "()", "(())()", and "(()(()))" are all valid parentheses strings.

A valid parentheses string S is primitive if it is nonempty, and there does not exist a way to split it into S = A+B,
with A and B nonempty valid parentheses strings.

Given a valid parentheses string S, consider its primitive decomposition: S = P_1 + P_2 + ... + P_k,
where P_i are primitive valid parentheses strings.

Return S after removing the outermost parentheses of every primitive string in the primitive decomposition of S.

Example 1:

    Input: "(()())(())"
    Output: "()()()"
    Explanation:
        The input string is "(()())(())", with primitive decomposition "(()())" + "(())".
        After removing outer parentheses of each part, this is "()()" + "()" = "()()()".


Example 2:

    Input: "(()())(())(()(()))"
    Output: "()()()()(())"
    Explanation:
        The input string is "(()())(())(()(()))", with primitive decomposition "(()())" + "(())" + "(()(()))".
        After removing outer parentheses of each part, this is "()()" + "()" + "()(())" = "()()()()(())".

Example 3:

    Input: "()()"
    Output: ""
    Explanation:
    The input string is "()()", with primitive decomposition "()" + "()".
    After removing outer parentheses of each part, this is "" + "" = "".

Note:

    S.length <= 10000
    S[i] is "(" or ")"
    S is a valid parentheses string
"""


class Solution(object):
    def removeOuterParentheses(self, S):
        """
        :type S: str
        :rtype: str
        """
        result = ''
        stack = []
        for s in S:
            if s == '(' and len(stack) >= 1:
                result += s

            if s == ')' and len(stack) >= 2:
                result += s

            if s == '(':
                stack.append(s)
            else:
                stack.pop()

        return result


if __name__ == '__main__':
    print(Solution().removeOuterParentheses("(()())(())"))
    print(Solution().removeOuterParentheses("(()())(())(()(()))"))
    print(Solution().removeOuterParentheses("()()"))
